[R] Random numbers negatively correlated?

[Thomas Lumley]

On Tue, 27 Jun 2006, Thomas Lumley wrote:

I got the table wrong, it should read

  x    1/0  1/1  est11
  000   -   -     -
  001   -   -     -
  010   1   0     0
  011   0   1     1
  100   1   0     0
  101   1   0     0
  110   1   1     0.5
  111   0   2     1

So the explanation is slightly more complicated. The problem is that 
although sum(x11==2)/n and sum(x11==2 | x11==(-1))/n are unbiased 
estimators their ratio is not an unbiased estimator, but has mean 5/12 
(which is 0.5-0.5/n).

 	-thomas